Question

The polar coordinates of the point whose cartesian coordinates are (−2, −2), are given by ____________.

Options

• `(2sqrt2, π/4)`

• `(2sqrt2, (7π)/6)`

• `(2sqrt2, (3π)/4)`

• `(2sqrt2, (5π)/4)`

Answer 1

The polar coordinates of the point whose cartesian coordinates are (−2, −2), are given by `underline((2sqrt2, (5π)/4)`.

Explanation:

Given coordinates (−2, −2)

∴ −2 = r cos θ and −2 = r sin θ

(−2)² = r² cos² θ and (−2)² = r² sin² θ

∴ 4 + 4 = r² (cos² θ + sin² θ)

r² = 8

r = `2sqrt2`

∴ cos θ = `(-2)/"r" = (-2)/(2sqrt2) = (-1)/sqrt2`

θ lie in 3^rd quadrant

∴ cos θ = `cos (π + π/4)`

θ = `(5π)/4`

∴ Polar coordinates `(2sqrt2, (5π)/4)`